In l987 and l988, the following scientific and engineering societies used for
the first time in society-wide elections an election reform called "approval
voting" (AV):

* The Mathematical Association of America (MAA), with about 30,000

members, in l987

* The Institute of Management Science (TIMS), with about 7,000

members, in l988

* The American Statistical Association (ASA), with about 15,000

members, in l988

* The Institute of Electrical and Electronics Engineers (IEEE), with

about 300,000 members, in l988

In addition, the Econometric Society has used AV (with certain emendations) to
elect fellows since l980 (Gordon, l98l); likewise, since l98l the selection of
members of the National Academy of Sciences (l98l) at the final stage of
balloting has been based on AV. Coupled with many colleges and universities
that now use AV--from the departmental level to the school-wide level--it is no
exaggeration to say that several hundred thousand individuals, mostly in the
sciences, have had direct experience with AV.

What is AV? We begin by providing a brief description of this election reform
and list some of the arguments that have been made for its adoption over
plurality voting (PV), the commonly used voting procedure under which voters
can vote for exactly one candidate. We then indicate the immediate factors
that led to the adoption of AV by the various societies. Next, we report on
the societies' recent experiences with AV--based on empirical analyses that we
with others have done of their ballot data in the different societies--and
compare these findings with theoretical results on AV. In general, we find
that AV can make a difference in the outcome of an election, elects majority
candidates who are not lowest common denominators, and usually mimimizes
ideological voting.

Approval Voting

AV, proposed independently by several analysts in the l970s, is a voting
procedure in which voters can vote for, or approve of, as many candidates as
they wish in multicandidate elections (i.e., those with more than two
candidates). Each candidate approved of receives one vote, and the candidate
with the most votes wins.

Advantages that proponents most often cite for AV are the following:

l. It gives voters more flexible options. They can do everything they
can under PV--vote for a single favorite--but if they have no strong preference
for one candidate, they can express this fact by voting for all candidates they
find acceptable. In addition, if a voter's most preferred candidate has little
chance of winning, that voter can vote for both a first choice and a
more viable candidate without worrying about wasting his or her vote on the
less popular candidate.

2. It will increase voter turnout. By being better able to express
their preferences, voters are more likely to vote in the first place. Voters
who think they might be wasting their votes, or who cannot decide which of
several candidates best represents their views, will not have to despair about
making a choice. By not being forced to make a single--perhaps
arbitrary--choice, they will feel that the election system allows them to be
more honest, which will make voting more meaningful and encourage greater
participation in elections.

3. It will help elect the strongest candidate. Today the candidate
supported by the largest minority often wins, or at least makes the runoff if
there is one. Under AV, by contrast, it will be the candidate with the
greatest overall support who will usually win. A related benefit is that AV
will induce candidates in campaigns to try to mirror the views of a majority of
voters, not just cater to minorities whose votes could give them a slight edge
in a crowded PV contest.

4. It will give minority candidates their proper due. Minority
candidates will not suffer under AV: their supporters will not be torn away
simply because there is another candidate who, though less appealing to them,
is generally considered a stronger contender. Because AV allows these
supporters to vote for both candidates, they will not be tempted to
desert the one who is perceived as weak, as under PV. Hence, minority
candidates will receive their true level of support under AV, even if they
cannot not win.

5. It is eminently practicable. Unlike more complicated ranking
systems, which suffer from a variety of theoretical as well as practical
problems (Brams and Fishburn, l983; Lijphart and Grofman, l984; Dummett, l984;
Nurmi, l987; Merrill, l988), AV is simple for voters to understand and use.
Although more votes must be tallied than under PV, tabulations on a computer
are hardly more time-consuming. More relevant to public elections, AV can
readily be implemented on existing voting machines; because it does not violate
any state constitutions in the United States (or the constitutions of most
countries in the world), it requires only a statute passed by a state
legislature to become law.

Under PV, a voter may switch to a second choice if his or her first choice
appears to be a long shot, as indicated, for example, by polls. By contrast,
AV encourages sincere voting--voting for all preferred candidates. However, AV
does not eliminate strategic calculations altogether. Because approval of a
less-preferred candidate could hurt a more-preferred candidate, the voter still
faces the decision under AV of where to draw the line between acceptable and
nonacceptable candidates.

Probably the best-known official elected by AV today is the secretary-general
of the United Nations (Brams and Fishburn, l983). Bills to implement AV have
been introduced in some state legislatures in the United States; in l987, a
bill to enact AV in certain statewide elections passed the Senate but not the
House in North Dakota. AV has been used in internal elections by the political
parties in some states, including Pennsylvania, where a presidential straw poll
using AV was conducted by the Democratic Party state committee in l983 (Nagel,
l984). In l990, Oregon used AV in a statewide advisory referendum on school
financing, in which voters could approve of one or more of five different
options on the ballot (Wright, l990).

Since l987, AV has been used in some competitive elections in Poland and the
Soviet Union, where it is in fact "disapproval voting" because voters are only
permitted to cross out names on ballots (Shabad, l987; Keller, l987, l988;
Mercik, l988; Federal Election Commission, l989; White, l989). But this
procedure is logically equivalent to AV: candidates not crossed out are, in
effect, approved. Psychologically, however, there is almost surely a
difference between approving and disapproving of candidates, but we know of no
studies documenting the effects of this difference on voter behavior.

The Adoption Decision in the Societies

Elections are not a burning issue in most scientific societies, with
participation rates often considerably below 50 percent of the membership. For
the candidates, on the other hand, who are often luminaries in their
disciplines, outcomes are usually more consequential and sometimes represent,
especially if the office is president, recognition of professional achievements
over one's career.

It is not surprising, then, that candidates are willing to make subdued
versions of what, in political life, would be called campaign statements. In
the more rarefied atmosphere of an academic or professional society, these
statements, which usually accompany a mailed ballot, tend more to emphasize
broad goals than specific programs, although candidates often pledge themselves
to undertake new initiatives. Most candidates, while listing their past
offices and qualifications for the new office, generally do not seek to
disparage the opposition.

Genteel as most of these campaigns are, candidates do, nonetheless, try to
garner support by highlighting their qualifications, and proposing new
approaches or ideas, that differentiate them from their opponents. When AV was
first proposed as a reform in the four societies that we studied, no candidates
or factions, with one major exception, identified it as a threat either to
their candidacies or points of view.

Of course, after AV's use, there are winners and losers, and some losers,
undoubtedly, see themselves as victims of this reform. In one society (TIMS),
as we shall show, this logic worked in reverse: the winner under PV, before AV
was adopted, would almost certainly have lost under AV--and this became an
argument made for the adoption of AV! We hasten to add that this was not a
personal argument directed against the PV winner; rather, the argument was that
this person was not the majority candidate, in a sense we shall make precise
later.

Separately, each of us played a role in the adoption of AV in three of the four
societies we studied. In all cases, we received considerable assistance from
others. We briefly recount the adoption decisions in the order in which the
societies first used AV:

l. The Mathematical Association of America. In l985, the president of
the MAA, Lynn Arthur Steen, who knew Brams and was familiar with work on AV,
told him that he wished the Board of Governors of the MAA to consider adoption
of AV in its biennial elections for president-elect and other national offices.
He asked Brams for information on AV, which Steen distributed to Board members.
After "heated but not acrimonious" debate (Steen, l985), AV was approved by the
Board in l985, passed by the membership in l986, and used for the first time in
the l987 MAA elections.

Steen earlier had written an article in Scientific American (Gardner,
l980) on the mathematics of elections, in which he discussed AV. Before the
MAA's consideration of AV, he had asked Brams to look into the use of the Hare
system of single transferable vote (STV) by the American Mathematical Society
(AMS), the major research society of mathematicians. (The MAA is the more
teaching-oriented of the two major mathematical societies at the
college-university level.) Brams (l982) demonstrated via two counterexamples
that the "Instructions to Voters" accompanying the l98l ballot used by the AMS
to elect a nominating committee contained an erroneous statement about a
property of STV. This statement was deleted from future instructions, but AV
was not seen by the AMS as preferable to STV to elect such a committee because
it is not a proportional-representation system suitable for multiple-winner
elections.

Both Steen's knowledge and his position as president of the MAA made him a
crucial player in the MAA's adoption of AV. So also was Steen's successor as
president of the MAA, Leonard Gillman, who was a strong advocate of AV and
played an active role in its eventual implementation in the l987 elections of
the Association. For example, he wrote a description of AV for mathematicians,
which included results of his own analysis (Gillman, l987).

2. The Institute of Management Sciences. The use of AV by TIMS in l988
was preceded by an experiment in which members were sent a nonbinding AV
ballot, along with the regular PV ballot, in the l985 elections. Although the
AV ballot did not count, 85 percent of the members who voted in these elections
returned the AV ballot. This permitted Fishburn and Little (l988) to compare
the results of voting under the two different systems.

On the basis of their empirical analysis, which we shall illustrate later, they
concluded that AV did a better job of electing majority candidates. Not only
was the experiment "remarkably successful" (Little and Fishburn, l986), but the
results also convinced TIMS Council to adopt AV in l987. In fact, an argument
for conducting the experiment in the first place was that management scientists
should "practice what we preach" (Jarvis, l984): before deciding on its usage,
TIMS should collect the information necessary to make an informed judgment
about the applicability of the theoretical analysis of AV to its own
elections.

Both the consideration and adoption of AV by TIMS were certainly helped by the
fact that the president of TIMS in l984-l985, John D. C. Little, was interested
in AV and collaborated with Fishburn on the experiment and its analysis.
Before undertaking the experiment, inquiries were made of the candidates to ask
their permission to participate in it. Because of its research potential, all
agreed, prefiguring AV's eventual adoption.

3. The American Statistical Association. Neither of us played any
personal role in the adoption of AV by the ASA. The chair of the ASA's
Committee on Elections, Richard F. Potthoff, had read about AV and brought it
to the attention of his committee. This committee recommended its adoption
first in "internal" ASA elections, and the ASA Board of Directors approved this
recommendation.

After AV's successful use in l986 in three elections for Council governors, the
election of two editors to serve on the Board, and the election of a Board
member to serve on the Executive Committee, the Committee on Elections
recommended that AV be used in the main ASA elections, which was approved by
the Board ("Amendment to ASA By-Laws," l987) and ratified as an amendment in
l987. Unlike the other societies, the ASA has had no Association-wide
multicandidate elections since the adoption of AV, though more internal
elections and some section elections have had more than two candidates.

4. The Institute of Electrical and Electronics Engineers. The adoption
of AV by the IEEE has a politically charged history (Brams and Nagel, l99l).
Beginning in l984, AV was considered, along with other voting systems, for
possible use in multicandidate elections. But not until the l986
elections--when a petition candidate, Irwin Feerst, ran against two candidates
for president-elect nominated by the Board of Directors--did the issue of
election reform take center stage. The reason is that Feerst, with 35 percent
of the vote, defeated one of the two Board-nominated candidates and came within
242 votes (of 52,405 cast) of defeating the other candidate. This result
starkly illustrated to the Board how vulnerable their nominees, who together
might win a substantial majority in an election, are to a minority candidate
if these nominees should split the majority vote more or less evenly.

In l987 the Board reverted to nominating only one candidate for
president-elect, breaking a tradition of nominating two candidates that it had
begun in l982. Feerst was instrumental in bringing the question of how many
nominees the Board must nominate to a vote of the entire membership in the l987
election, in which he did not run and there were no other petition candidates.
By a 57-percent majority, members supported a constitutional amendment
requiring that the Board nominate at least two candidates, but this fell short
of the 2/3's majority needed to amend the IEEE's constitution.

Nevertheless, it was clear that there was strong membership support for making
IEEE elections more competitive, which renewed interest in AV should the Board
return to nominating two candidates and petition candidates also run. Brams,
who had contacted the IEEE after the l986 election and recommended
consideration of AV, was invited in l987 by the president of the IEEE, Henry L.
Bachman, to attend an Executive Council meeting to discuss AV. He could not
attend but suggested that Jack H. Nagel, who had done extensive research on AV,
take his place. Nagel not only substituted but also later attended a meeting
of the full Board of Directors, which adopted AV in November l987. (AV had
previously been used in internal IEEE elections, sometimes in modified form.)
With its adoption, the Board voted to nominate at least two candidates for each
office.

When the IEEE's adoption of AV was announced at a December l987 IEEE press
conference in New York City that Brams and Nagel attended, Feerst objected
strenuously to its use, arguing that it was a deliberate move to undermine his
candidacy and the interests of "working engineers," whom he claimed to
represent. When Feerst ran in l988 for president-elect under AV, he came in
fourth in a field of four candidates.

To recapitulate, the paths to adoption of AV in the different societies have
been diverse. Only in the MAA did full-scale use of AV begin before it was
first tried out in an experiment (TIMS) or in internal elections (ASA and
IEEE).

The presidents of the MAA and TIMS played active roles in AV's adoption in
their societies, and each received assistance from one of us. In the ASA, on
the other hand, neither of us was directly involved, though our writings on AV
sparked initial interest, which turned into adoption without much
controversy.

Controversy was the hallmark of the IEEE deliberations, and Brams and Nagel
were actively involved. Brams's involvement began when he read a news report
in Science ("Briefing: Feerst in Close Call," l987) describing the
election that Feerst almost won, at which point he contacted Bachman. While
the IEEE's adoption of AV was in part a response to a perceived threat to its
established leadership, it is important to realize that the IEEE did not view
it as its only alternative.

In fact, several other election systems had been considered before Brams
contacted Bachman, including AV. Afterwards, although AV became the focus of
discussions, it was not the only reform put forward. For example, a runoff
election between the two top contenders, if neither received a majority in the
initial balloting under PV, was also seriously considered, but it was viewed as
too costly to have a second round of voting and also would have required a
constitutional change. Ultimately, a majority of Board members concluded that
AV better fit the needs of the organization than any other voting system, and
that is why it was adopted. [By no means do we imply that AV is a pancea in
all elections, especially those involving multiple winners; for such elections,
see the AV-related reforms in Brams (l990), Brams and Fishburn (l99l), and
Fishburn and Brams (l99l).] Although questions have been raised about AV's
possible conflict with the not-for-profit law of New York State which governs
the IEEE (Brams and Nagel, l99l), no court challenges to AV have been mounted.

This quick overview does not do justice to the serious debates that occurred
over the merits of AV, particularly in the MAA and the IEEE. Indeed, dissent
over AV's use continues in some societies (Kiely, l99l), so it is appropriate
to look at what AV has wrought in them.

Does Approval Voting Make a Difference?

Clearly, a new voting procedure makes a difference if it leads to the
selection of a different winner. The best evidence we have that AV would have
elected a different winner is from the l985 TIMS experiment, in which ballot
data for both the PV official elections and the AV nonbinding elections were
compared (Fishburn and Little, l988).

In one of the three l985 elections, the official PV and actual AV ballot totals
are shown in Table l for candidates A, B, and C. Also shown are the

____________________________________________________________

Table l about here

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AV totals extrapolated from the 85-percent sample of members who returned their
AV nonbinding ballots, which is a very high figure. The extrapolation is a
straightforward one: approval votes are added to the actual AV totals for each
candidate based on the propensity of the sample respondents who voted for one
particular candidate on the PV ballot to vote for each of the other candidates
on the AV ballot. This extrapolation is justified by the finding that there
are no major differences in voting patterns on the official PV ballot between
AV respondents and nonrespondents.

Observe that candidate C wins the official PV election by a bare 8 votes (0.4
percent), but B would have won under AV by a substantial l70 votes (6.l
percent). By itself, the fact that C wins more plurality votes and B wins more
approval votes does not single out one candidate as the manifestly preferred
choice. But on the experimental ballot, voters were asked one piece of
additional information: to rank-order the candidates from best to worst by
marking next to their names l for their first choice, 2 for their second
choice, and so on.

These data can be used to reconstruct who would defeat whom in hypothetical
pairwise contests, which is not evident from the PV totals. For example, the
fact that B edges out C in presumed first choices, based on the PV totals, does
not mean that B would hold his or her lead when the preferences of the l66 A
voters are taken into account. In fact, the experimental ballots of these l66
voters show that

l. 70 provided rankings in the order ABC;

2. 66 provided rankings in the order ACB;

3. 3 provided no rankings but approved both A and B;

4. 27 made no distinctions between B and C by rankings or approval.

In the B-versus-C comparison, it is reasonable to credit (l) and (3) to B (73
votes), (2) to C (66 votes), and (4) to neither candidate. When added to the
PV totals, these credits give C (90l votes) exactly one more vote than B (900
votes). However, assuming the 27 voters in (4) split their votes between B and
C in the pattern of the l39 voters (70 + 66 + 3) who ranked A first and also
expressed a preference between B and C, B would pick up an additional vote
(rounded to the nearest vote), resulting in a 9l4-9l4 tie.

This extrapolation indicates that there is not a single majority candidate,
sometimes designated a Condorcet candidate (Condorcet, l785), who would
defeat all the other candidates in pairwise contests. (In most elections there
is such a candidate, and AV almost always elects this person, as both
theoretical analysis and computer simulation demonstrate and several real-life
elections illustrate (Brams and Flishburn, l983; Nurmi, l987; Merrill, l988).)
While surprising, the lack of a single Condorcet candidate should not obscure
the fact that l70 more voters approved of B rather than C, albeit C won the PV
contest by 8 votes.

The reason for this discrepancy between the AV and PV results is that whereas C
has slightly more stalwart supporters (i.e., those who vote only for one
candidate) than B, supporters of the third candidate, A, more approve of B than
C (36% to 23%). Furthermore, because more of C's supporters approve of B than
B's do of C, B would have won handily under AV.

Is this desirable? In the absence of a Condorcet candidate, Fishburn and
Little (l988) concluded in their report on this election that

approval voting picks a clear winner on the basis of second choices.

These show that B has a broader acceptance in the electorate than C.

Therefore, the approval process, by eliciting more information from

the voters, leads to the election of the candidate with the widest

support.

To be sure, it is theoretically possible in close elections that the Condorcet
candidate will not be the most approved candidate. Although we have yet to
discover empirically a clash between these two criteria, the legitimacy of the
AV winner may be questioned on other grounds.

Does Approval Voting Elect the Lowest Common Denominator?

One fear that has been expressed about the use of AV is that while itmay help elect candidates more broadly representative than PV, these
candidates could turn out to be rather bland and uninspiring. They may win
simply because they offend the fewest voters, not because they excite the
passions of many.

It is difficult to say whether, in principle, a compromise candidate is a
better or worse social choice than a more extreme candidate who is the darling
of some voters but the bane of others. In practice, fortunately, this
dichotomous choice seems rarely to arise, as the data from the four societies'
AV elections demonstrate. Specifically, the winners under AV were candidates
who were generally popular among all voters, however many candidates
they voted for in the different elections. Thus, a divergence between forceful
minority candidates, approved of by few, and "wishy-washy" majority candidates,
approved of by many, may well be an infrequent event.

There are, however, examples of elections in which the winner was not strong
among all classes of voters. Consider the l987 MAA election shown in Table 2
(Brams, l988), wherein the votes received by the five candidates
____________________________________________________________

Table 2 about here

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in this election are broken down by the votes each of the candidates received
from voters' casting exactly one vote (l-voters), voters' casting exactly two
votes (2-voters), and so on. Excluded from these totals are 9 voters who voted
for all the candidates, whose undifferentiated support obviously has no effect
on the outcome.

In this election, 3,08l of the 3,924 voters (79 percent) were l-voters, while
the remaining 843 voters cast l,956 votes, or an average of 2.3 votes each.
Thus, the multiple voters cast 39 percent of the votes, though they
consitituted only 2l percent of the electorate.

Did the multiple voters make a difference? It would appear not, because the
winner (A) received 28% more votes from l-voters than the runner-up (D), just
edged out B among 2-voters, but lost to several candidates among 3-voters and
among 4-voters. A's victory, then, is largely attributable to the substantial
margin received from l-voters, not from the presumably more lukewarm support
received from multiple voters.

Define a candidate who wins among all classes of voters--those who cast few
votes (narrow voters) and those who cast many votes (wide

voters)--as AV-dominant. In the MAA contest, for example, we might
assume narrow voters are those who cast l or 2 votes, and wide voters are those
who cast 3 or 4 votes. Then A is not AV-dominant because he or she wins among
narrow but not among wide voters.

Does this vitiate A's winning status? Winning so decisively among l-voters,
whose preference intensities would seem to be greatest, it would be hard to
argue that A is any kind of lowest commong denominator. It should be noted,
however, that some of the 37 voters who voted for four of the five candidates
probably also had intense preferences--but against the one candidate they chose
to leave off their approved lists.

We found that in l2 of the l6 multicandidate AV elections we analyzed, the
winners were AV-dominant. In the four elections in which there was not an
AV-dominant winner, the pattern is similar to that in the l987 MAA election
shown in Table 2: the winner won by virtue of receiving greater support among
narrow voters than among wide voters. These AV-nondominant winners, therefore,
do not fit the mold of lowest common denominators--the choice of many wide
voters but few narrow voters--but rather the opposite, which reinforces, not
undermines, their legitimacy as winners.

The fact that the winners in three-quarters of the elections were AV-dominant
is perhaps not surprising because one would expect such candidates would do
better than losers across different types of voters. A little reflection,
however, shows that this need not be the case. Paradoxically, a candidate may
lose among every possible class of voters--that is, be AV-dominated--and
still be the AV winner. For example, A might be the victor over C among narrow
voters, and B might be the victor over C among wide voters. But C could emerge
as the AV winner if A did badly among wide voters, B did badly among narrow
voters, but C was a close second among both types.

No winners in the l6 elections were AV-dominated. As already noted, even the
support of the four AV-nondominant winners appeared to be more intense and
heartfelt (i.e., from narrow voters) than that of the losers.

If AV is adopted in public elections, it is hard to predict whether AV-dominant
candidates would be the norm. It is certainly conceivable that a moderate
could garner enough support from both left-oriented and right-oriented
voters--who might prefer candidates on the left and right--to win, without
receiving much exclusive support from centrist voters. This would tend to be
the case when the center is relatively weak, which might be an argument for
electing a moderate, wo can then mediate between the extremes. Since we have
yet to observe such a case empirically, however, we hesitate to say whether
approval voting would serve such a moderating purpose, or should.

Is Voting "Ideological"?

Consider again the l987 MAA election. We have drawn Venn diagrams
indicating the shared support among the l0 subsets of two candidates, l0 of
three candidates, 5 of four candidates, and l of all five candidates. These
are not shown here, but as can be calculated from Table 2, 2-voters gave the
candidates 22-26% of all their votes, 3-voters l0-l6%, and 4-voters 2-5%.
Examination of the sources of this support (shown in the Venn diagrams)
does not reveal any particular pairs, triples, or quadruples that received
unusually great support, indicating that there was not obvious coalitional
voting.

On the contrary, multiple votes are spread about as one would expect according
to the null hypothesis that votes are distributed in proportion to the
candidates totals. In the case of A, for example, there were 82 shared votes
with just B, 9l with just C, 80 with just D, and 23 with just E, which is
roughly in accord with the candidates's overall totals. Indeed, every one of
the 32 subsets in this election--including the 2.6 percent who abstained --got
at least 3 votes.

The story is very different for the l988 IEEE election shown in Table 3

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Table 3 about here

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(Brams and Nagel, l99l), where we have indicated the approval vote totals for
all l6 subsets of the four candidates in this race. Consider first the
3-voters, and note that nearly everyone in this category voted for ABD--5,605,
to be precise. By contrast, only l48, l43, and 89 voters, respectively,
supported the other 3-subsets of ABC, ACD, and BCD that contain C. Evidently,
the numerous supporters of ABD voted against C by voting for everybody except
C. This essentially negative kind of voting against C can also be seen in
voting for the six 2-subsets. The three 2-subsets that do not include C (AB,
AD, and BD) had an average of 4,027 voters each, whereas the three that
included C (AC, BC, and CD) had an average of only 897 voters each.

In addition to the predominant clustering of support around A, B, and D, there
are some subtle differences in the sharing of support. For each pair of
candidates, Brams and Nagel (l99l) computed an index of shared support by
taking the ratio of ballots approving both candidates by 2-voters and 3-voters
to total ballots, excluding abstentions and votes for all four candidates. By
this measure, A and D have the most affinity, with 22.9% shared support. They
are followed by A and B, with l7.2%; and then by B and D, with l3.9%. Although
A, B, and D share much less support with C, B at 3.l% shares slightly more with
him than do A (l.8%) and D (l.5%).

From these results, one might infer an underlying dimension on which D and C
occupy opposite extremes, whereas A and B are located at intermediate
positions. A is somewhat closer than B to D, but both B and A are much closer
to D than to C, as shown in the following hypothetical continuum:

l___l_____l_________________________________________l

D A B
C

This representation corresponds to certain facts about the candidates. D and A
were both Board nominees, whereas C was a vigorous critic of IEEE officers,
Board, and staff. B, though like C a petition candidate, was in other ways
close to the IEEE establishment, having previously served on the Board. As for
the slight distinction between D and A, judging from the candidates'
biographies and statements it may reflect D's emphasis on technical research,
which perhaps made him seem most distant from C, who sought to champion the
"working engineer."

Of the 54,204 ballots analyzed in this election, only 3,323 (6.l%) are
"inconsistent" with the assumption that voters' preferences are based on the
DABC ordering of candidates. Inconsistent ballots include approval of
two nonadjacent candidates without including the adjacent candidate(s) between
them, notably DC (608), AC (659), DAC (l43), and DBC (89). Accounting for more
than half the inconsistencies is the relatively minor inconsistency--in terms
of perceived differences--represented by the pattern DB (l,824). Of the
multiple voters, l7,435 (84.0%) cast ballots consistent with the hypothetical
ordering.

Thus, candidates with obvious affinities tended disproportionately to share
approval from multiple voters. In this sense voting was ideological: it
reflected a pattern consistent with an underlying ordering of the candidates.
Only in this election, however, did we find such a strong pattern; far more
typical, it seems, voting in the societies is nonideological, which is
consistent with the null hypothesis alluded to earlier. We suspect, however,
that if AV were used in public elections, their more political character would
often lead to the kind of ideological cleavages we observed in the IEEE
election.

It is important to note, however, that nonideological voting may mirror
regularities not evident in the AV data themselves. As a case in point, the
winner in the l987 MAA election (Table 2) was a woman, and this pattern was
repeated in the next MAA election in l989. We have not analyzed data from the
latter election, but the l987 winner's victory, as we showed earlier, cannot be
impeached on grounds that she won mostly because of lukewarm support from wide
voters. Nonetheless, as the only women in each of the two races, it may be the
case that they were helped by their uniqueness: by some they were perceived as
the single best choice; by others they were seen as broadly acceptable.

To avoid the "uniqueness factor," it may be advisable to include additional
women in such contests--or additional other types who may be identifiable
because of such characteristics as race, religion, or nationality. Because AV
is relatively insensitive to the size of the field, increasing the number of
candidates in this manner should have few if any adverse effects at the same
time that it diminishes the effect of what may be regarded as extraneous or
idiosyncratic factors.

Summary

Approval voting has proved to be a practical and viable election reform
in the four scientific and engineering societies, collectively comprising some
350,000 members, that used it for the first time in l987 and l988. We played a
role in its adoption in three of the four societies (TIMS, MAA, and IEEE), but
we were not even aware of its consideration in the fourth society (ASA) until
its adoption was imminent.

In all the societies, AV's adoption rested principally on arguments supporters
of AV have made that is it a more democratic procedure than PV in
multicandidate elections. In the IEEE, a petition candidate's near-win with
vocal but only minority support certainly gave urgency to these arguments,
accelerating AV's adoption after the Board's attempt to limit the number of
Board-nominated candidates to one met with the membership's disapprobation.

The empirical analyses of election returns from the different societies
indicate that AV may make a difference. So far it seems not to have elected
candidates who can be characterized as lowest common denominators but instead
candidates who either enjoyed support among all classes of voters or who did
particularly well among narrow voters, whose support we presume to be more
intense. Majority or Condorcet candidates, insofar as they can be ascertained,
invariably won. In theory this may not always occur, or there may not even be
a single such candidate, as was illustrated in the l985 TIMS election
experiment. Finally, we found that voting was generally nonideological, but in
one IEEE election a clear ordering of positions could be identified, and voting
tended to be only for adjacent candidates in this ordering.

*We thank our coauthors, Jack H. Nagel and John D. C. Little, of the cited
articles on which this paper is in part based, Kalyan Chatterjee, and anonymous
referees. Brams gratefully acknowledges the financial support of the National
Science Foundation under grant SES-87l537.

Abstract

Approval voting is a voting system in which voters can vote for as many
candidates as they like in multicandidate elections. In l987 and l988, four
scientific and engineering societies, collectively comprising some 350,000
members, used this election reform for the first time. Their reasons for
adoption varied but centered around efforts to elect consensus candidates.
Approval voting has indeed elected so-called Condorcet candidates, who can
defeat all other candidates in pairwise contests. Moreover, these winners
generally enjoy support among different classes of voters, so they are not
merely "lowest common denominators," as some analysts had feared. In at least
one instance, approval voting would have led to a different winner from
plurality voting (in which voters can vote for exactly one candidate);
arguably, this winner would have been the better social choice because he had
wider support than his closest opponent. On another occasion, approval voting
led to "ideological voting"--in which the voting patterns reflected an
underlying ordering of the candidates--but voting in most societies tends to be
nonideological. Overall, the recent experimentation with approval voting has
shown that it not only may make a difference but also elects broadly acceptable
candidates.